ABSTRACT
This chapter focuses on the use of the elliptic operator as a means of generating computational grids for irregular physical domains. It begins by presenting some of the properties of the Laplacian elliptic operator. The chapter explores how the source term, or terms, provide control over smoothness of the interior grid and packing of coordinate lines near boundaries. It introduces the Poisson equation methods for grid generation. The chapter begins by providing a qualitative understanding of the effect of the nonhomogeneous term in the case of a one-dimensional grid. Elliptic grid generation, as opposed to other differential methods such as hyperbolic and parabolic, has been widely used for several reasons. For bounded domains, the boundary functions mapping the physical boundaries to the logical boundaries result in boundary fitted coordinates. The chapter concludes with a presentation of various control functions.
